"I feel good," said Cruise, who spent nearly an hour greeting fans before walking the red carpet. "It's like making a movie. You get a couple hours' sleep. You get up and get back at it."

The stars – who attended their first red carpet at 6:30 a.m. in London and then flew to Paris and then to New York – traveled on one plane with other cast members and director Doug Liman for the first leg. That "was a lot of fun," said Cruise, who, with Blunt, spent much of that flight walking around and socializing.

When it was time to fly from Paris to New York later that day, Cruise, Blunt and Liman, who "bonded" while making the film, the director said, took their own plane.

"We hung out for a bit and then just crashed," said Cruise, who looked crisp in a custom-fit black suit, white shirt and black tie.

"I don't know what happened on the other plane," he joked. "Emily and I were on ours, kind of going, 'We don't want to know. What happened on that plane stays on that plane.' ... We'll find out later."

Blunt, who looked stunning in a red strapless Prada column gown in New York City, had less-glamorous travel attire for the final flight. "I wore really disgusting pajamas," she said. "Me and makeup artist snuggled up together. I slept for four hours. It was great."

Before the movie, which opens to the public on Friday in the U.S., Blunt hit the gym "maybe twice a week," but upped her workouts to six days a week, two and a half hours a day, to train for the physical demands of battling alien invaders in the film.

"That was very new to me," she said.

That might come in handy one day, when her daughter Hazel, 3 months, gets older.

"I hope she knows not to mess with me if she's being a bad teenager," said the new mom. "She'll know if she's watched this movie."